Functional Harmony operates from the assumption that each chord in a progression has a particular purpose within that progression.
This purpose is refered to as the chord's function.

The three basic functions are:

tonic - chords of rest and resolution

sub-dominant - chords of movement

dominant - chords of tension, which move or resolve to tonic

Diatonic Functional Harmony

Tonic

Sub-Dominant

Dominant

Imaj7 VIm7 [IIIm7]
Cmaj7 Am7 [Em7]

IVmaj7 IIm7
Fmaj7 Dm7

V7
G7

The function of a chord is determined by the scale degrees contained in the chord.
The three principal scale degrees used in determining the chords function are the first, fourth and seventh degrees.

Chords which contain the first scale degree but not the fourth are considered tonic.
Chords which do not contain, nor support as a tension,
the fourth scale degree are also considered tonic,
even if they don't contain the first scale degree (as in Em7 in the key of C).

Imaj7, VIm7, IIIm7

Chords which contain the fourth scale degree but not the seventh are considered sub-dominant.
The chord must include the first scale degree as a chord tone,
or allow the first scale degree as a tension,
and may include the seventh scale degree as a tension if the first scale degree is present as a chord tone
(this is true for both diatonic sub-dominant chords).

IVmaj7, IIm7

Chords which contain the seventh scale degree but not the first are considered dominant,
if the chord can support the fourth scale degree as a chord tone.

V7, VIIm7b5

Non-diatonic chords can be classified using the same qualifications.
Note that using substitution chords
(one purpose for functional areas)
requires that the proper
melody-harmony relationship be maintained.